one half of the water is poured out of a full container. then one third of the remainder us poured out Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, etc. After how many pourings does exactly one ninth of the origiNl water remain?

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05-12-2022
Mathematics

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one half of the water is poured out of a full container. then one third of the remainder us poured out Continue the process: one fourth of the remainder for the third pouring, one fifth of the remainder for the fourth pouring, etc. After how many pourings does exactly one ninth of the origiNl water remain?

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saishreechandan907 saishreechandan907 · Answer 1 · 2022-12-07T22:34:23-05:00

Exactly one-ninth of the original water is left after 8 pourings.

Given data,

Model the container's remaining contents as follows;

After the first pour, 1⁄2 is left, after the second, half * two-thirds, etc.

This is the final result. 1/2 * 2/3 * 3/4 * . . . . 8/9 * 9/10

Because the terms cancel out, 9/10 remains.

The numerators form an arithmetic sequence with a common difference of 1 and endpoints (1, 8), thus all that is left to do is count the terms or pour.

Therefore, 8 pourings do exactly one-ninth of the original water remain.

To learn more about arithmetic sequence click here:

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